Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #4208⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #4208⋊D5 |
| Fitting, derived, Hall | C5×#737 ⋊ C22 |
| Sylow | #737 ⋊ C2×D5 |
| Sylow | C5 ⋊ #4207⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×#737 | C22 |
| Frattini | C3 | C5⋊#1113 |
| socle | C3×C5 | #1113 |
| LCS | G ▷ C5×#737 | |
| UCS | C1 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2^2,3^3,5,3|d^3=g^2,c^a=c^2,d^a=d^2g,f^a=f^4,g^a=g^2,c^b=c^2,e^b=e^2,e^c=eg81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4207⋊C2, #72247520 |
| maximal normal subgroup of | D5×#4207⋊C2, #72247520 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 355);